Add broth; bring to a simmer over medium-high heat. Reduce heat to low and simmer, partially covered, until cauliflower is tender, about 10 minutes.

Using an immersion blender or traditional blender, puree until very smooth, 30 seconds to 1 minute. (If using a traditional blender, vent it either by removing the lid's pop-out center or by lifting one edge of the lid. Drape the blender canister with a kitchen towel. To 'clean' the canister, pour in a little half-and-half, blend briefly, then add to the soup.)